B Is Everything in the Expanding Universe Growing Along with It?

[Gedanken]

If the Universe is expanding, wouldn't it be common sense to think everything inside it is expanding too?

 

[Morgan Patranella]

No. the space in between objects is expanding but not the objects like Earth themselves... This is what you asked, correct?

 

[Comeback City]

And to add on, this is pretty much just happening at the intergalactic level.

 

[David Lewis]

If spacetime is expanding then new heres and nows are being created.

 

[Drakkith]

If the Universe is expanding, wouldn't it be common sense to think everything inside it is expanding too?

The expansion of the universe is about the distance between objects increasing over time. Note my choice of words there. The distance between objects. Objects bound together by strong forces, such as the atoms in molecules or planets to their stars, are not expanding as far as we know. But, given a large enough distance, these forces drop off far enough to allow expansion to take place and the objects get further away from each other over time.

 

[PeterDonis]

If spacetime is expanding then new heres and nows are being created.

This is not correct. Spacetime is a 4-dimensional manifold; it already contains all "heres" and "nows". "Expanding" just labels a particular feature of the geometry of this 4-dimensional manifold.

Also, since as far as we can tell spacetime is a continuum, even if we adopt a particular coordinate chart (such as standard FRW coordinates), expansion does not create new "space" in these coordinates. Each "point in space" can be labeled in FRW coordinates and the labels are the same at every instant of time.

 

[Albrecht]

I have not really understood this. If the space expands, do fields like the electrical field and the gravitational field expand by the same amount? - That would mean that any objects and also galaxies expand in the same way as the space and are so unchanged in relation to the space.

 

[rede96]

I have not really understood this. If the space expands, do fields like the electrical field and the gravitational field expand by the same amount? - That would mean that any objects and also galaxies expand in the same way as the space and are so unchanged in relation to the space.

It is true, at least according to the dark energy model, that expansion does exert a very small ‘negative pressure’ on objects which causes them to expand more than they would without the pressure from expansion. But the effects are so small I don’t think it’s possible to measure on such small scales. And in any case it’s no where near enough to overcome the forces that hold objects together.

 

[Albrecht]

I do not mean any pressure or any force.
If there is for instance relativistic contraction (in SRT) then there is contraction for all objects and for all fields and for everything. There is no force involved. - My question is whether expansion in case of the whole universe is the same or is it different so that the distances of objects expand but fields of any kind do not change.

 

[phinds]

I have not really understood this. If the space expands, do fields like the electrical field and the gravitational field expand by the same amount? - That would mean that any objects and also galaxies expand in the same way as the space and are so unchanged in relation to the space.

No, it would not mean that at all. Again, objects on the order of galactic clusters and smaller do not expand. EM radiation BETWEEN such bound systems does change. Light drops in frequency and loses energy when traveling between bound systems.

 

[my2cts]

No, it would not mean that at all. Again, objects on the order of galactic clusters and smaller do not expand. EM radiation BETWEEN such bound systems does change. Light drops in frequency and loses energy when traveling between bound systems.

Interesting discussion. Are you saying that electromagnetic fields inside atoms do not expand but such fields in between galaxy clusters, galaxies, stars perhaps or even planets , do ? At what scale does this transition from expansion to non-expansion occur ?

 

[Drakkith]

The value of the field at any particular point in space will likely change as expansion causes charges to move away from each other, but whether or not that means that the "field itself" is expanding is difficult to answer.

 

[PeterDonis]

If the space expands, do fields like the electrical field and the gravitational field expand by the same amount?

Fields don't have a size, so asking whether or not they expand makes no sense.

That would mean that any objects and also galaxies expand in the same way

Since you are starting from a mistaken premise, you can't expect to reason correctly from it.

If your question is whether bound systems expand due to the universe's expansion, the answer has already been given in this thread: no.

If there is for instance relativistic contraction (in SRT) then there is contraction for all objects and for all fields and for everything.

For objects, yes. Fields don't have a size so they can't "contract". The components of fields are affected by a Lorentz transformation, yes, just like the components of any vector or tensor.

My question is whether expansion in case of the whole universe is the same

No. You're trying to compare apples and haircuts. They're not even the same kind of thing.

Length contraction is an effect of changing your choice of coordinates.

Expansion of the universe is a way of describing the overall spacetime geometry of the universe in terms of the behavior of the worldlines of comoving objects.

the distances of objects expand but fields of any kind do not change

The distances between comoving objects increase. That has nothing to do with the behavior of any fields (at least as far as I can tell what you mean by that term; you don't seem to be using it in the usual way).

At what scale does this transition from expansion to non-expansion occur ?

There is no "transition". The spacetime geometry of the universe is what it is. Comoving objects have particular worldlines in this geometry. Individual parts of bound systems (like stars in a galaxy or planets in a solar system) have other worldlines. That's all there is to it. You can't pick out regions and say that "expansion" is happening in some but not others. Once you've described all the worldlines of objects and the geometry of spacetime, you've described everything; there's nothing left over.

 

[PeroK]

Interesting discussion. Are you saying that electromagnetic fields inside atoms do not expand but such fields in between galaxy clusters, galaxies, stars perhaps or even planets , do ? At what scale does this transition from expansion to non-expansion occur ?

Expansion is only measurable on large scales. If you do the calculation then the expansion between the Earth and Sun is about 10m per
year.

The Earth, however, cannot keep drifting further away each year. Instead, gravity and any expansion settle into a stable equilibrium, with expansion slightly reducing the effect of gravity.

The Earth's orbit, therefore, is slightly larger than it would be if there were no expansion.

In this case, the solar system is gravitationally bound. Which means gravity is the dominant factor.

At an intermediate scale - The Milky Way and Andromeda galaxies say - although still gravitationally bound, the effects of expansion would be more noticeable.

On a larger scale, the gravity between distant galaxies is so small compared to the expansion that gravity becomes negligible and you have effectively only expansion.

 

[Bandersnatch]

Expansion is only measurable on large scales. If you do the calculation then the expansion between the Earth and Sun is about 10m per year.

The Earth, however, cannot keep drifting further away each year. Instead, gravity and any expansion settle into a stable equilibrium, with expansion slightly reducing the effect of gravity.

The Earth's orbit, therefore, is slightly larger than it would be if there were no expansion.

In this case, the solar system is gravitationally bound. Which means gravity is the dominant factor.

Looks like you're using Hubble's law for these calculations. I.e. you took the Hubble constant, and calculated the Hubble flow for 1 AU, which over 1 year gives about 10 metres.
It's not the right way to go about, as you're mixing expansion with acceleration. Expansion by itself (w/o dark energy) is similar to inertial motion, rather than a force - i.e. it can't make Earth's orbit larger. The 10 m/year increase is what you'd get if only if the Earth and the Sun were moving with the Hubble flow. They aren't - they're gravitationally bound. They had long decoupled from the Hubble flow, which has as much bearing on the size of Earth's orbit today as the velocity of gas particles in the molecular cloud from which the Solar system coalesced. There's no equilibrium to talk about with expansion (without DE).

What does increase the orbit is dark energy, but that's many orders of magnitude less pronounced than what you calculated. At 1 AU it should result in acceleration of something like $~10^{-25} m/s^2$. Compare with centripetal acceleration in Earth's orbit: $~10^{-2} m/s^2$.
So, unless I borked the calculations, that means the orbit is one picometre larger than it'd be without it.

But again, that's the effect of DE. Without it, the expansion itself wouldn't have any effect.

 

[PeroK]

Looks like you're using Hubble's law for these calculations. I.e. you took the Hubble constant, and calculated the Hubble flow for 1 AU, which over 1 year gives about 10 metres.
It's not the right way to go about, as you're mixing expansion with acceleration. Expansion by itself (w/o dark energy) is similar to inertial motion, rather than a force - i.e. it can't make Earth's orbit larger. The 10 m/year increase is what you'd get if only if the Earth and the Sun were moving with the Hubble flow. They aren't - they're gravitationally bound. They had long decoupled from the Hubble flow, which has as much bearing on the size of Earth's orbit today as the velocity of gas particles in the molecular cloud from which the Solar system coalesced. There's no equilibrium to talk about with expansion (without DE).

What does increase the orbit is dark energy, but that's many orders of magnitude less pronounced than what you calculated. At 1 AU it should result in acceleration of something like $~10^{-25} m/s^2$. Compare with centripetal acceleration in Earth's orbit: $~10^{-2} m/s^2$.
So, unless I borked the calculations, that means the orbit is one picometre larger than it'd be without it.

But again, that's the effect of DE. Without it, the expansion itself wouldn't have any effect.

Fair enough, but you then still have to answer the question at which point do you transition from a gravitationally bound system to one where expansion applies.

How far from the Sun must you be to measure a non-zero recessional red-shift?

 

[PeroK]

PS the $10m$ per annum clearly doesn't equate to a $10m$ increase in orbit I could equally well have calculated the hypothetical expansion per second, which would be a fraction of a metre.

 

[PeterDonis]

The Earth's orbit, therefore, is slightly larger than it would be if there were no expansion.

No, it's very, very, very slightly larger than it would be if there were no dark energy. In an expanding universe with zero dark energy the size of the Earth's orbit would be unaffected by the expansion.

In this case, the solar system is gravitationally bound. Which means gravity is the dominant factor.

At an intermediate scale - The Milky Way and Andromeda galaxies say - although still gravitationally bound, the effects of expansion would be more noticeable.

On a larger scale, the gravity between distant galaxies is so small compared to the expansion that gravity becomes negligible and you have effectively only expansion.

None of this is correct as regards expansion in the absence of dark energy.

at which point do you transition from a gravitationally bound system to one where expansion applies.

There is no such "transition". See the last paragraph of my post #13.

 

[Albrecht]

For objects, yes. Fields don't have a size so they can't "contract". The components of fields are affected by a Lorentz transformation, yes, just like the components of any vector or tensor.

Yes, fields can contract, and that is (as you say) described by the Lorentz transformation.

And you can measure the contraction. If you have a charge, then at a distance r from the charge you may have a field strength E. If now the field contracts (by whatever cause) by a factor of 2, then at the position r you will measure a field of E/4. That is a clear indication of the contraction.

This is particularly visible for multipole fields like the electrical fields in objects. The molecules in an object are bound to each other by electrical multipole fields. The size of the object is mostly given by the extension of these fields. So, if the object contracts in motion (special relativity) then this is only possible because the fields contract. This causes for instance the MM apparatus to contract in motion and that causes, as we know, the null result of that experiment.

A similar thing happens in a gravitational field. If space contracts which contains a gravitational field, also objects contract there because the binding fields inside contract.

Now cosmology tells us that the space of the universe expands. That is the opposite to contraction but understood to be fundamentally the same phenomenon like relativistic contraction. And if it is the same phenomenon then the rules and consequences have to be similar. But this would now mean that also gravitational fields expand, and so the size of planetary orbits has to increase and also the size of galaxies, as the constituents of a galaxy are bound gravitationally to each other.

So the assumption that the distance of galaxies (which are maintained by inertia and so fixed to the space) on the one hand and the size of galaxies on the other hand behave differently (as some has said in this discussion) does not look logical.

 

[PeterDonis]

If you have a charge, then at a distance r from the charge you may have a field strength E. If now the field contracts (by whatever cause) by a factor of 2, then at the position r you will measure a field of E/4.

Please give a reference for the experimental results that demonstrate this.

Please note that I am not disputing that electromagnetism is consistent with SR; of course it is. I am asking for a specific experimental situation that merits the description "the field contracts" as you have described it, in order to justify the further claims you are making.

A similar thing happens in a gravitational field. If space contracts which contains a gravitational field, also objects contract there because the binding fields inside contract.

Same comment here: please give a reference for the specific experimental results that demonstrate this.

cosmology tells us that the space of the universe expands.

No, it doesn't. That is pop science, not real science. Real cosmology tells us that comoving objects in our universe are moving apart. That is not the same as "space expands".

That is the opposite to contraction but understood to be fundamentally the same phenomenon like relativistic contraction.

No, it isn't. It has nothing to do with length contraction in SR.

The rest of your post just builds on these misconceptions.

 

[my2cts]

Expansion is only measurable on large scales. If you do the calculation then the expansion between the Earth and Sun is about 10m per
year.

Small but nonzero. What is not measurable today, is tomorrow. See the LIGO case.

The Earth, however, cannot keep drifting further away each year. Instead, gravity and any expansion settle into a stable equilibrium, with expansion slightly reducing the effect of gravity.

Indeed. Expansion of a hydrogen atom, or the orbit of the Earth, requires energy.
However that argument holds at any scale.

The Earth's orbit, therefore, is slightly larger than it would be if there were no expansion.

Do you have a reference for this ?

 

[PeroK]

Expansion of a hydrogen atom, or the orbit of the Earth, requires energy.
However that argument holds at any scale.

Do you have a reference for this ?

See the comments above. The difference, if there is one, would be immeasurably small.

I still think you are missing the point that - even if hypothetically the solar system or a hydrogen atom was "trying" to expand - the other factors would simply override this. I think you are looking for an ongoing unstoppable expansion at scales below which the expansion of the universe is not a relevant factor.

 

[my2cts]

See the comments above. The difference, if there is one, would be immeasurably small.

Define immeasurable. Besides immeasurable is not the same as nonexistent. We cannot measure planets in distant galaxies, but we know they are there.

I still think you are missing the point that - even if hypothetically the solar system or a hydrogen atom was "trying" to expand - the other factors would simply override this. I think you are looking for an ongoing unstoppable expansion at scales below which the expansion of the universe is not a relevant factor.

"trying" to expand ? And how would "other factors [] override this"?
I hope you mean conservation of energy and momentum.
That's my point.

 

[PeterDonis]

Expansion of a hydrogen atom, or the orbit of the Earth, requires energy.

You are sweeping a lot of complexities under the rug. That's not a good idea. Even though this is a "B" level thread, we still have to pay attention to the fact that there are more advanced details.

 

[PeroK]

Define immeasurable. Besides immeasurable is not the same as nonexistent. We cannot measure planets in distant galaxies, but we know they are there."trying" to expand ? And how would "other factors [] override this"?
I hope you mean conservation of energy and momentum.
That's my point.

Let's say you dropped a 1kg ball from a height of 10m. Technically, the Earth moves a small distance. But, that's immeasurable, not least because lots of other things are happening around the Earth at the same time. You can't stop all other changes that are happening to try to measure something as small as that - even if, theoretically, you could measure a distance of that magnitude, which I doubt.

The same is true of the Earth's orbit. There are changes and variations due to the gravity of everything in the solar system. These effects will be many orders of magnitude larger than the expansion of space on the scale of the Solar system. Jupiter, for example, moves the Sun about the same as the Sun's diameter over a year. That's a variation of about $1.5$ million $km$ in the position of the Sun. How do you set up an experiment to measure a change of, say, $1mm$ in amongst that? It's absurd. It's immeasurable.

 

[my2cts]

You are sweeping a lot of complexities under the rug. ... there are more advanced details.

Please specify the complexities and more advanced details, if necessary with references.
Keep the quality of this

"B" level thread"

up !

 

[my2cts]

There are changes and variations due to the gravity of everything in the solar system. These effects will be many orders of magnitude larger than ...

than for example the effect gravitational waves.
"Attempting to measure a change in arm length 1,000 times smaller than a proton means that LIGO has to be " etc.
https://www.ligo.caltech.edu/page/ligos-ifo
Yet LIGO measures GWs.
Immeasurability is a practical problem and does not imply non-existence.

 

[PeroK]

"Attempting to measure a change in arm length 1,000 times smaller than a proton means that LIGO has to be " etc.
https://www.ligo.caltech.edu/page/ligos-ifo
Yet it works.

That's a "controlled" environment. The solar system is not.

 

[my2cts]

That's a "controlled" environment. The solar system is not.

I would need a definition of that as well.
LIGO is a tool to observe systems much less "controlled" than the solar system, namely coalescing black holes. It does not get any worse.
Besides, whether physicists are able to measure it or not, is irrelevant to the question if cosmic expansion implies expansion of atomic hydrogen or of the Earth's orbit. That is a different thread.
I think here the question is: does cosmic expansion expand literally everything to expand or only really large stuff. A related question is: if anything expands cosmologically, does this increase its energy ?

 

[PeterDonis]

Please specify the complexities and more advanced details, if necessary with references.

Not in a "B" level thread; that's why I pointed out the thread level. If you are genuinely curious about the complexities, please start a separate thread at the "I" or "A" level.

 

[my2cts]

Not in a "B" level thread; that's why I pointed out the thread level. If you are genuinely curious about the complexities, please start a separate thread at the "I" or "A" level.

I am fully aware of the physical complexities and advanced features of atoms and the solar system, by the way.
I just challenge that they are relevant here.
Still, I was unaware that the threads have actual levels. My mistake.
My argument ends here and now as I don't do "B" discussions.

 

[PeroK]

"trying" to expand ? And how would "other factors [] override this"?

Okay, here's a thought. Hydrogen atoms formed when the universe was much smaller than it is now. Let's assume that these atoms expand as the universe does. So, these hydrogen atoms today would be several times larger than they were when they formed. So:

Hypothesis: there are hydrogen atoms of all different sizes, depending on when they formed. Ones that formed in the early universe would be larger than ones that formed more recently - having expanded with time.

Is there any evidence for hydrogen atoms of different sizes? No. The energy levels (which are implied by the "distance" between the electron and the nucleus) are standard.

Theoretically, a hydrogen atom can only exist in certain discrete energy levels. The atom cannot exist in some intermediate state, caused by an expansion. The atom is either in one energy level or the next. It can't slowly expand into a continuous series of intermediate energy levels.

Therefore, the hydrogen atom cannot expand, regardless of what space is "trying" to do to it.

Note that the same would be true of, say, stars themselves. Even if stars "tried" to expand due to spatial expansion, gravity would just immediately pull everything back together again.

It's the same if the Earth "tries" to drift away from the Sun: gravity just won't let it go!

 

[PAllen]

I'll give my standard 'rant' on this. Expanding universe just means there is always room for comoving bodies to continue moving away from each other, not that space is pushing them, or that two 'positions' are moving apart (except in particular coordinates). Also, there is no difference in origin between the redshift between two distant comoving bodies versus a similar red shift between two distant arbitrary non-comoving bodies in the same universe. In each case, relative motion in GR is fundamentally ambiguous, but redshift between distant bodies is a function of curvature between them and what their motions are.

An analogy is lines drawn up from the apex of a cone, with the apex down. Consider the vertical time, with circles being slices for each cosmic time. Without doubt, the circles grow with cosmic time. However, angles (motion) between lines originating at the apex (comoving observers) is no different from angles between arbitrary lines on the cone. Further, two lines that start parallel will remain parallel. That successive circles are larger in no way causes lines that start parallel to move apart. This feature corresponds to what has been alluded to that without dark energy, if you had two small bodies far apart in a giant void that happen not to have any red shift between them, then even over cosmic time scales, they will continue to have no redshift, and the radar distance between them will not grow, irrespective of their not being bound.

The case of dark energy can be analogized by assuming the cone flares out from the apex. Then, two lines that start parallel will diverge, due to the hyperbolic geometry. In this geometry, if two lines remain constant distance, at least one must not be a geodesic. In the GR case with dark energy, this means that for two distant small bodies in a giant void to remain constant distance, at least one must be non-inertial. Similarly, there is a tiny affect on gravitationally bound systems.

 

[Albrecht]

Please give a reference for the experimental results that demonstrate this.

In my knowledge there do not exist any real experiments, in which contraction was directly proven. But contraction has to be assumed in special relativity to avoid conflicts. So it follows indirectly from dilation and the constancy of c. As well the contraction of fields. - One can find this in every textbook about special relativity. My favorite is: A.P French, "Special Relativity".
If space would contract in motion but fields would not follow this, then the principle of relativity should be violated. Because the observer in a moving system would see different conditions than an observer at rest.

 

[Albrecht]

Same comment here: please give a reference for the specific experimental results that demonstrate this.

The same situation here. Contraction follows indirectly.
Imagine a light clock in a gravitational field. The time indication of such clock has to show the dilation which happens there. This can only work correctly if (1) the speed of light is reduced as given by GRT and (2) the distance of the mirrors is reduced.
Again: any different behaviour would violate the principle of relativity.

 

[Albrecht]

No, it doesn't. That is pop science, not real science. Real cosmology tells us that comoving objects in our universe are moving apart. That is not the same as "space expands".

Sorry but I have learned that differently. Wrong? In my knowledge Lemaitre has used Einstein's general concept of space to describe the development of the universe. He has related the expansion to space. - Not true? And in the discussions about Dark Energy, the argument (also in univerity discussions) is always that the "extension of space" goes on in an accelerated way. Stars are only measured to proof this.

 

[Albrecht]

No, it isn't. It has nothing to do with length contraction in SR.

The rest of your post just builds on these misconceptions.

It was my understandig of Einstein that he has developed a generel concept about space. Also in his later papers about, what he called "new ether", he discussed general properties of the space and did not differentiate between the space in SRT, in GRT, or in cosmology.

 

[rede96]

Expanding universe just means there is always room for comoving bodies to continue moving away from each other, not that space is pushing them, or that two 'positions' are moving apart (except in particular coordinates).

Comoving bodies are moving away from each other but the two ' positions' are not moving apart. Could you explain what you mean by this?

 

[PeroK]

Comoving bodies are moving away from each other but the two ' positions' are not moving apart. Could you explain what you mean by this?

Try this:

https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

 

[rede96]

Try this:

https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

Thanks for the link. If we imagine galaxies plotted on some come cosmic size coordinate system then yes I understand that the galaxies are at rest wrt that coordinate system (comoving galaxies) and the points on the coordinate grid are moving further apart (expansion).

But what I was interested in is what is powering the expansion of the grid? I understood dark energy to be a sort of negative 'pressure' that caused expansion but it seems most tend to model expansion as objects "free falling" like in a gravitational field, just away from each other.

What confused me is that in Leonard Susskind's lectures on cosmology he does describe dark energy as a kind of negative pressure and not as a type of anti-gravity. In fact he describes all bound systems being very slightly and equally effected by expansion in that the the point of equilibrium the systems end up in is very slightly more expanded then it would be without dark energy. (excuse my poor terminology!)

Hence my confusion to this:

not that space is pushing them

as that's exactly how I understood it. That dark energy was applying a negative pressure to matter / energy and causing matter in non bound systems to move apart.

 

[PeroK]

Thanks for the link. If we imagine galaxies plotted on some come cosmic size coordinate system then yes I understand that the galaxies are at rest wrt that coordinate system (comoving galaxies) and the points on the coordinate grid are moving further apart (expansion).

But what I was interested in is what is powering the expansion of the grid? I understood dark energy to be a sort of negative 'pressure' that caused expansion but it seems most tend to model expansion as objects "free falling" like in a gravitational field, just away from each other.

What confused me is that in Leonard Susskind's lectures on cosmology he does describe dark energy as a kind of negative pressure and not as a type of anti-gravity. In fact he describes all bound systems being very slightly and equally effected by expansion in that the the point of equilibrium the systems end up in is very slightly more expanded then it would be without dark energy. (excuse my poor terminology!)

Hence my confusion to this: as that's exactly how I understood it. That dark energy was applying a negative pressure to matter / energy and causing matter in non bound systems to move apart.

That would be normal positive pressure. A model where a gas is expanding and pushing things with it. That's not what's happening here.

Negative pressure means that energy is required to expand the vacuum - rather than energy required to compress it.

Note that vacuum energy is positive: if a vacuum expands and its energy density remains constant - as it must, assuming vacuum is vacuum and you can't dilute a vacuum - then that implies more total energy.

The other energies (matter and radiation) have the obvious property that as space expands, their energy densities must decrease. Vacuum energy has what seems the extraordinary property that this does not happen and, as space expands, the total vacuum energy goes up and up.

As I understand it, that is where we reach the mystery of dark energy.

 

[PAllen]

Comoving bodies are moving away from each other but the two ' positions' are not moving apart. Could you explain what you mean by this?

Simple. Comoving bodies, by any reasonable definition, are moving away from each. Meanwhile, position has no meaning beyond coordinate choice in relativity. Consider just SR: every distinct frame entails a different definition of what constant position means, and they are all equally valid. Constant position cannot possibly have more meaning in GR than it does in SR. Expansion is the feature of spacetime geometry that makes it possible for comoving bodies to continue moving apart. Using my simple 1x1 analogy, if the universe is cone shaped, you are able to have comoving bodies moving apart forever. A cylinder, or a cone whose sides bent to asymptote a cylinder would not allow this.

Specifically, it is trivial to define constant position such that positions don't move apart. Pick a particular galaxy. Define that world lines that show no redshift as seen by this galaxy are lines of constant position. Just as valid as any other choice. No matter how far away some other comoving galaxy is, if a light source in that galaxy is moving towards us with a speed relative to that galaxy (this relative velocity, being local, is well defined) corresponding to the galactic redshift interpreted as SR Doppler, then light from that source will show no red shift. Define constant position lines by such light sources rather than comoving galaxies. Even with Dark Energy, this is still possible, but such light sources will need to move more and more non-inertially to maintain absence of redshift as observed by us, the more Dark Energy there is. But as long as we can see a comoving object, there is colocated non-superliminal velocity trajectory which would have no redshift as observed by us.

Note, this is also a justification why I consider the phrase "superluminal recession velocities" misleading.

 

[PAllen]

Hence my confusion to this: as that's exactly how I understood it. That dark energy was applying a negative pressure to matter / energy and causing matter in non bound systems to move apart.

Note, I stated the same as Susskind, that with Dark energy there is tiny shift of equilibria even for bound systems. The difference in how we phrase interpretation is a matter of which side of an equation we are focusing on. Assuming you put the cosmological constant on the right hand side of the GR field equation (e.g. to allow the possibility for it to be a dynamical field rather than a constant), then as a field contributing to stress energy it has a natural interpretation as negative pressure. However, possibly paradoxically, the effect of negative pressure on the metric corresponding the Einstein tensor (the left hand side of the equation) is to produce a homogeneous tendency of geodesics to diverge (and positive pressure produces the opposite gravitational effect). To me, this is just as much gravity as the tendency of geodesics in Schwarzschild spacetime to converge in two directions while diverging in the third. Gravity is effect of the metric tensor on inertial stucture. Negative pressure produces a certain form of gravity.

 

[PeterDonis]

space would contract in motion

"Space" doesn't contract in SR. Objects appear to have shorter lengths to observers moving relative to them.

but fields would not follow this

Once again: I agree that electromagnetism is consistent with SR. That's not the issue. The issue is that you are using the word "contraction" to refer to how electromagnetic fields transform under a Lorentz transformation. That word is not appropriate because fields do not have a "length" or a "size", so they can't contract. So there's no point in you continuing to say that SR has to be valid; nobody is disputing that. You need to show what property of fields can be properly said to be a "length" and to "contract".

Imagine a light clock in a gravitational field. The time indication of such clock has to show the dilation which happens there. This can only work correctly if (1) the speed of light is reduced as given by GRT and (2) the distance of the mirrors is reduced.

You are confused. Spacetime is curved in the presence of gravity. You are trying to use intuitions from SR, that only work in flat spacetime, in the presence of gravity. That doesn't work.

Also, the "speed of light" you refer to is a coordinate speed, not a physical speed. You don't appear to understand the distinction; it's crucial.

I have learned that differently.

From where? Can you give an actual textbook or peer-reviewed paper as a reference?

It was my understandig of Einstein that he has developed a generel concept about space.

Where are you getting this understanding from? Again, can you give an actual textbook or peer-reviewed paper as a reference?

Einstein developed GR as a theory of spacetime, not space.

in his later papers about, what he called "new ether", he discussed general properties of the space and did not differentiate between the space in SRT, in GRT, or in cosmology.

Are these actual peer-reviewed papers, or popular articles? Please give specific references.

 

[Albrecht]

Once again: I agree that electromagnetism is consistent with SR. That's not the issue. The issue is that you are using the word "contraction" to refer to how electromagnetic fields transform under a Lorentz transformation. That word is not appropriate because fields do not have a "length" or a "size", so they can't contract. So there's no point in you continuing to say that SR has to be valid; nobody is disputing that. You need to show what property of fields can be properly said to be a "length" and to "contract".

Fields cannot contract? How can you say this?
Example: There may be a field E of a charge q described by the equation: E = q/r². Then assume that conditions change so that now there is E = q/(2r). So, if one looks to the spatial distribution of the field, the field (i.e. its shape) is contracted by a factor of 2. What is the problem here?

Historically Oliver Heaviside has in 1888 deduced from the Maxwell equations that an electrical field contracts for a moving charge by the equation E --> E' = E / gamma, where gamma = sqrt(1/(1-v²/c²)). This was a well known result and an important step towards relativity.

This fact of a "contraction of a field" is well known and was never questioned by the physical community to my knowledge.

 

[Albrecht]

You are confused. Spacetime is curved in the presence of gravity. You are trying to use intuitions from SR, that only work in flat spacetime, in the presence of gravity. That doesn't work.

Also, the "speed of light" you refer to is a coordinate speed, not a physical speed. You don't appear to understand the distinction; it's crucial.

Of course I know the distinction. All this is the view of an observer from outside the field. For the observer in the field there is no difference visible. This is demanded by the principle of relativity.

First about time: There is time dilation in a gravitational field. An observer can put a clock into the field and after a time take it back again. The clock in the field compared to a clock which stayed outside is retarded according to the dilation formula for gravity. And now the case of contraction; here again as said for SRT: the contraction can only be determined indirectly. I have proposed the case of a light clock. This light clock has to represent the dilation in gravity. And this dilation can only be explained if contraction is assumed and a reduction of the speed of light. Where speed of light means of course the coordinate value. And that is appropriate because all this is viewed by an observer outside the field.

You say correctly that space-time is curved. This curvature includes of course the contraction of space in the radial direction for a radial field (like for a star). In case of the light clock the calculation depends on the orientation of the clock.

 

[Albrecht]

Where are you getting this understanding from? Again, can you give an actual textbook or peer-reviewed paper as a reference?

Einstein developed GR as a theory of spacetime, not space.

That is in general correct. But as said before: in a radial field or in general in a radial situation curvature means contraction.
And in the case of the expanding universe: this is also a radial situation and so the change of the space means expansion.

 

[Albrecht]

Are these actual peer-reviewed papers, or popular articles? Please give specific references.

Einstein died in 1955. So there are no actual papers from him.

In the years 1925 until 1955 he developed his understanding of space which means his understanding of those properties of the space which he called the "new ether". He published a series of papers and also books about this topic. I do not know which of his papers were peer-reviewed. But I know that Einstein did not like this peer-reviewing. Because he said "I am Einstein and any peer-reviewing is inappropriate".

I do not have a list of his papers and books about this topic at hand. But university libraries should have them.

 

[PeterDonis]

Fields cannot contract? How can you say this?

Because, as I have said several times and you have apparently not grasped, "fields contract" is not the same as "fields transform according to Lorentz transformations". You keep giving arguments for the latter. Those are not arguments for the former.

Oliver Heaviside has in 1888 deduced from the Maxwell equations that an electrical field contracts for a moving charge by the equation E --> E' = E / gamma

Which does not describe "contraction" unless E is a length. Which it isn't. It describes the relativistic transformation of the field strength when you change frames. Field strength is not length.

 

[PeterDonis]

There is time dilation in a gravitational field. An observer can put a clock into the field and after a time take it back again. The clock in the field compared to a clock which stayed outside is retarded according to the dilation formula for gravity.

Yes.

Where speed of light means of course the coordinate value. And that is appropriate because all this is viewed by an observer outside the field.

No, it's not appropriate because it's just a coordinate effect. No physics can depend on how you choose your coordinates.

This curvature includes of course the contraction of space in the radial direction

No, it doesn't. The coordinate effect you are describing is not "contraction of space". It's just a coordinate effect. No physics can depend on how you choose your coordinates.

If you actually look at the "space" in question, and compare it to a Euclidean space enclosed by a 2-sphere with the same surface area, you will find that it is more appropriate to describe the "space" around a massive body as "expanded" rather than "contracted"; the 3-volume enclosed by a 2-sphere of a given surface area is larger if there is a gravitating mass inside the 2-sphere than if there is only vacuum there.

in a radial field or in general in a radial situation curvature means contraction.

No, it doesn't. See above.

in the case of the expanding universe: this is also a radial situation and so the change of the space means expansion.

I'm not sure what you mean by "a radial situation". The universe is homogeneous; spacetime around a gravitating mass is not. They're not the same.

Also, as I have already said, the expansion of the universe is not properly described as a "change of space".